Single-Particle Momentum Distribution of an Efimov trimer

Experimental progress in the study of strongly interacting ultracold atoms has recently allowed the observation of Efimov trimers. We study theoretically a non-conventional observable for these trimer states, that may be accessed experimentally, the momentum distribution n(k) of the constitutive bosonic particles. The large momentum part of the distribution is particularly intriguing: In addition to the expected 1/k^4 tail associated to contact interactions, it exhibits a subleading tail 1/k^5 which is a hall-mark of Efimov physics and leads to a breakdown of a previously proposed expression of the energy as a functional of the momentum distribution.Comment: This is a subpart of the (too long to be published) work arXiv:1001.0774. This subpart has 11 pages and 2 figures. Revised version correcting minor error

Exact relations for quantum-mechanical few-body and many-body problems with short-range interactions in two and three dimensions

We derive relations between various observables for N particles with zero-range or short-range interactions, in continuous space or on a lattice, in two or three dimensions, in an arbitrary external potential. Some of our results generalise known relations between large-momentum behavior of the momentum distribution, short-distance behavior of the pair correlation function and of the one-body density matrix, derivative of the energy with respect to the scattering length or to time, and the norm of the regular part of the wavefunction; in the case of finite-range interactions, the interaction energy is also related to dE/da. The expression relating the energy to a functional of the momentum distribution is also generalised, and is found to break down for Efimov states with zero-range interactions, due to a subleading oscillating tail in the momentum distribution. We also obtain new expressions for the derivative of the energy of a universal state with respect to the effective range, the derivative of the energy of an efimovian state with respect to the three-body parameter, and the second order derivative of the energy with respect to the inverse (or the logarithm in the two-dimensional case) of the scattering length. The latter is negative at fixed entropy. We use exact relations to compute corrections to exactly solvable three-body problems and find agreement with available numerics. For the unitary gas, we compare exact relations to existing fixed-node Monte-Carlo data, and we test, with existing Quantum Monte Carlo results on different finite range models, our prediction that the leading deviation of the critical temperature from its zero range value is linear in the interaction effective range r_e with a model independent numerical coefficient.Comment: 51 pages, 5 figures. Split into three articles: Phys. Rev. A 83, 063614 (2011) [arXiv:1103.5157]; Phys. Rev. A 86, 013626 (2012) [arXiv:1204.3204]; Phys. Rev. A 86, 053633 (2012) [ arXiv:1210.1784

General relations for quantum gases in two and three dimensions. Two-component fermions

We derive exact relations for $N$ spin-1/2 fermions with zero-range or short-range interactions, in continuous space or on a lattice, in $2D$ or in $3D$, in any external potential. Some of them generalize known relations between energy, momentum distribution $n(k)$, pair distribution function $g^{(2)}(r)$, derivative of the energy with respect to the scattering length $a$. Expressions are found for the second order derivative of the energy with respect to $1/a$ (or to $\ln a$ in $2D$). Also, it is found that the leading energy corrections due to a finite interaction range, are proportional to the effective range $r\_e$ in $3D$ (and to $r\_e^2$ in $2D$) with exprimable model-independent coefficients, that give access to the subleading short distance behavior of $g^{(2)}(r)$ and to the subleading $1/k^6$ tail of $n(k)$. This applies to lattice models for some magic dispersion relations, an example of which is given. Corrections to exactly solvable two-body and three-body problems are obtained. For the trapped unitary gas, the variation of the finite-$1/a$ and finite $r\_e$ energy corrections within each $SO(2,1)$ energy ladder is obtained; it gives the frequency shift and the collapse time of the breathing mode. For the bulk unitary gas, we compare to fixed-node Monte Carlo data, and we estimate the experimental uncertainty on the Bertsch parameter due to a finite $r\_e$.Comment: Augmented version: with respect to published version, subsection V.K added (minorization of the contact by the order parameter). arXiv admin note: text overlap with arXiv:1001.077

Mobility and stability of large vacancy and vacancy-copper clusters in iron: An atomistic kinetic Monte Carlo study

The formation of Cu-rich precipitates under irradiation is a major cause for changes in the mechanical response to load of reactor pressure vessel steels. In previous works, it has been shown that the mecha- nism under which precipitation occurs is governed by diffusion of vacancy-copper (VCu) complexes, also in the absence of irradiation. Coarse-grained computer models (such as object kinetic Monte Carlo) aimed at simulating irradiation processes in model alloys or steels should therefore explicitly include the mobil- ity of Cu precipitates, as a consequence of vacancy hops at their surface. For this purpose, in this work we calculate diffusion coefficients and lifetimes for a large variety of VCu complexes. We use an innovative atomistic model, where vacancy migration energies are calculated with little approximations, taking into account all effects of static relaxation and long-range chemical interaction as predicted by an interatomic potential. Our results show that, contrary to what intuition might suggest, saturation in vacancies tend toslow down the transport of Cu atoms.Fil: Castin, N.. Centre d’Etudes de l’énergie Nucléaire; BélgicaFil: Pascuet, Maria Ines Magdalena. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Malerba, L.. Centre d’Etudes de l’énergie Nucléaire; Bélgic

Coherence time of a Bose-Einstein condensate

Temporal coherence is a fundamental property of macroscopic quantum systems, such as lasers in optics and Bose-Einstein condensates in atomic gases and it is a crucial issue for interferometry applications with light or matter waves. Whereas the laser is an "open" quantum system, ultracold atomic gases are weakly coupled to the environment and may be considered as isolated. The coherence time of a condensate is then intrinsic to the system and its derivation is out of the frame of laser theory. Using quantum kinetic theory, we predict that the interaction with non-condensed modes gradually smears out the condensate phase, with a variance growing as A t^2+B t+C at long times t, and we give a quantitative prediction for A, B and C. Whereas the coefficient A vanishes for vanishing energy fluctuations in the initial state, the coefficients B and C are remarkably insensitive to these fluctuations. The coefficient B describes a diffusive motion of the condensate phase that sets the ultimate limit to the condensate coherence time. We briefly discuss the possibility to observe the predicted phase spreading, also including the effect of particle losses.Comment: 17 pages, 8 figures; typos correcte

Pair-Breaking Collective Branch in BCS Superconductors and Superfluid Fermi Gases

We demonstrate the existence of a collective excitation branch in the pair-breaking continuum of superfluid Fermi gases and BCS superconductors. At zero temperature, we analytically continue the equation on the collective mode energy in Anderson's Random Phase Approximation or Gaussian fluctuations through its branch cut associated with the continuum, and obtain the full complex dispersion relation, including in the strong coupling regime. The branch exists as long as the chemical potential $\mu$ is positive and the wave number below $\sqrt{2m\mu}/\hbar$ (with m the fermion mass). In the long wavelength limit, the branch varies quadratically with the wave number, with a complex effective mass that we compute analytically for an arbitrary interaction strength.Comment: 6-7 pages, 4 figures, in English et en fran\c{c}ai

Dynamical Instability of a Rotating Dipolar Bose-Einstein Condensate

We calculate the hydrodynamic solutions for a dilute Bose-Einstein condensate with long-range dipolar interactions in a rotating, elliptical harmonic trap, and analyse their dynamical stability. The static solutions and their regimes of instability vary non-trivially on the strength of the dipolar interactions. We comprehensively map out this behaviour, and in particular examine the experimental routes towards unstable dynamics, which, in analogy to conventional condensates, may lead to vortex lattice formation. Furthermore, we analyse the centre of mass and breathing modes of a rotating dipolar condensate.Comment: 4 pages, including 2 figure

Exact mean field concept to compute defect energetics in random alloys on rigid lattices

In modern materials science modeling, the evolution of the energetics of random alloys with composition are desirable input parameters for several meso-scale and continuum scale models. When using atomistic methods to parameterize the above mentioned concentration dependent function, a mean field theory can significantly reduce the computational burden associated to obtaining the desired statistics in a random alloy. In this work, a mean field concept is developed to obtain the energetics of point-defect clusters in perfect random alloys. It is demonstrated that for a rigid lattice the concept is mathematically exact. In addition to the accuracy of the presented method, it is also computationally efficient as a small box can be used and perfect statistics are obtained in a single run. The method is illustrated by computing the formation and binding energy of solute and vacancy pairs in FeCr and FeW binaries. Also, the dissociation energy of small vacancy clusters was computed in FeCr and FeCr-2%W alloys, which are considered model alloys for Eurofer steels. As a result, it was concluded that the dissociation energy is not expected to vary by more than 0.1 eV in the 0?10% Cr and 0?2% W composition range. The present mean field concept can be directly applied to parameterize meso-scale models, such as cluster dynamics and object kinetic Monte Carlo models.Fil: Bonny, G.. Sck-Cen Centre Detude de Lénergie Nucléaire; FranciaFil: Castin, N.. Sck-Cen Centre Detude de Lénergie Nucléaire; FranciaFil: Pascuet, Maria Ines Magdalena. Comision Nacional de Energía Atómica; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Çelik, Y.. Sck-Cen Centre Detude de Lénergie Nucléaire; Franci

Quantum backreaction in dilute Bose-Einstein condensates

For many physical systems which can be approximated by a classical background field plus small (linearized) quantum fluctuations, a fundamental question concerns the correct description of the backreaction of the quantum fluctuations onto the dynamics of the classical background. We investigate this problem for the example of dilute atomic/molecular Bose-Einstein condensates, for which the microscopic dynamical behavior is under control. It turns out that the effective-action technique does not yield the correct result in general and that the knowledge of the pseudo-energy-momentum tensor ${<\hat T_{\mu\nu}>}$ is not sufficient to describe quantum backreaction.Comment: 8 pages of RevTex4; extended discussion with additional sections, to be published in Physical Review

Finite Size Effect on Correlation Functions of a Bose Gas in a Trap and Destruction of the Order Parameter by Phase Fluctuations

The influence of the finite sizes on the coherent properties of 3D Bose systems is considered. As is shown, the correlation functions of a Bose gas in a trap have essential differences from analogous correlation functions in an infinite system. Thus, the anomalous correlation function vanishes due to the divergency of phase fluctuations which destruct the order parameter too. The normal correlation function decays exponentially in time for sufficiently large time interval.Comment: 10 pages, RevTex4, some references have been added some changes in text are mad